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This problem in geometry has been solved in no less than EIGHT ways
by a pair of students. How would you solve it? How many of their
solutions can you follow? How are they the same or different? Which
do you like best?

A loopy exploration of z^2+1=0 (z squared plus one) with an eye on
winding numbers. Try not to get dizzy!

Twizzles Venture Forth

Stage: 4 Challenge Level:

In this animation, the you can change the value of the blue twizzle
z . The red twizzle takes
the value (z-i) . The
green twizzle takes the value (z+i) . The grey twizzle takes the
value (z-i)(z+i) . You can
check that by multiplying the red and green twizzles using
Twizzle Arithmetic . You need to know that i is the name we give the twizzle
which has a number arrow equal to the unit arrow but rotated
through 90 degrees.

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the
NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to
embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities
can be found here.